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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 728 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.4x + 5y = −57 and 5x + 4y = −60 →
  2. 2.x + 3y = 36 and 3x + 6y = 81 →
  3. 3.6x − 5y = −34 and 4x + 3y = −10 →
  4. 4.3x + 2y = 45 and 6x + 3y = 81 →
  5. 5.5x + 4y = −13 and 5x + 6y = −27 →
  6. 6.6x − 6y = −36 and x + 6y = 57 →
  7. 7.6x + 3y = 60 and 5x + 4y = 62 →
  8. 8.6x − 3y = −33 and 3x − 2y = −21 →
  9. 9.3x + y = 29 and x + 3y = 23 →
  10. 10.7x + 9y = 88 and 9x + 7y = 72 →
  11. 11.7x + 2y = 51 and 2x + 7y = 66 →
  12. 12.2x + y = 13 and 3x + y = 18 →
  13. 13.5x − 5y = 55 and 4x + 3y = −19 →
  14. 14.3x + 2y = 3 and 3x + 5y = 21 →
  15. 15.5x + 5y = 55 and 4x + 5y = 47 →
  16. 16.6x + 3y = 33 and 3x + 2y = 17 →
  17. 17.x + 2y = 11 and 5x + 6y = 47 →
  18. 18.8x + 6y = 36 and 6x + 8y = 34 →
  19. 19.3x − 6y = 39 and x + 2y = −3 →
  20. 20.6x − 6y = −24 and 5x + 6y = −9 →
  21. 21.5x + 7y = −42 and 7x + 5y = −54 →
  22. 22.4x + 5y = 10 and 5x + 4y = −1 →
  23. 23.9x + 5y = 42 and 5x + 9y = 42 →
  24. 24.4x + 4y = 56 and 2x + 3y = 37 →
  25. 25.2x − 2y = 18 and 2x + 3y = −7 →
  26. 26.x + 4y = 17 and 4x + y = 38 →
  27. 27.6x + 4y = −24 and 2x + 4y = −16 →
  28. 28.2x + y = −5 and 5x + 5y = −10 →
  29. 29.5x + 9y = 83 and 9x + 5y = 71 →
  30. 30.2x + 6y = −24 and 3x + 4y = −31 →
  31. 31.3x + 3y = 15 and 4x + 6y = 26 →
  32. 32.4x + 2y = 24 and 4x + 4y = 36 →
  33. 33.6x + 5y = 31 and 5x − 3y = 33 →
  34. 34.x + 6y = −43 and 6x + y = −13 →
  35. 35.9x + 6y = 6 and 6x + 9y = 39 →
  36. 36.2x + 2y = −2 and 4x − 2y = 8 →
  37. 37.5x + 5y = 15 and 4x + 6y = 0 →
  38. 38.2x + 3y = 22 and 6x + 6y = 60 →
  39. 39.6x + 4y = 62 and 4x + 6y = 68 →
  40. 40.6x + 8y = 78 and 8x + 6y = 62 →

Answer key

  1. x = −8, y = −5
  2. x = 9, y = 9
  3. x = −4, y = 2
  4. x = 9, y = 9
  5. x = 3, y = −7
  6. x = 3, y = 9
  7. x = 6, y = 8
  8. x = −1, y = 9
  9. x = 8, y = 5
  10. x = 1, y = 9
  11. x = 5, y = 8
  12. x = 5, y = 3
  13. x = 2, y = −9
  14. x = −3, y = 6
  15. x = 8, y = 3
  16. x = 5, y = 1
  17. x = 7, y = 2
  18. x = 3, y = 2
  19. x = 5, y = −4
  20. x = −3, y = 1
  21. x = −7, y = −1
  22. x = −5, y = 6
  23. x = 3, y = 3
  24. x = 5, y = 9
  25. x = 4, y = −5
  26. x = 9, y = 2
  27. x = −2, y = −3
  28. x = −3, y = 1
  29. x = 4, y = 7
  30. x = −9, y = −1
  31. x = 2, y = 3
  32. x = 3, y = 6
  33. x = 6, y = −1
  34. x = −1, y = −7
  35. x = −4, y = 7
  36. x = 1, y = −2
  37. x = 9, y = −6
  38. x = 8, y = 2
  39. x = 5, y = 8
  40. x = 1, y = 9

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